MATH 110 WEEK6 TEST
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American Military University *
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Course
110
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
5
Uploaded by zeidameehan
Back Logout Advanced Functions & Logarithms Exam
Report a mistake Filter By 90% View answer 1. What is the inverse function of the f(x) = �
2? f−1(x) = 2x
f−1(x) =
�
2 f−1(x) = x + 2
f−1(x) = x
−
2 f−1(x) = 2x + 2
View answer 2. What is the inverse function of the f(x) = 3
�
+15?
f−1(x) =
5
�
+33
f−1(x) =
5
�
−33
f−1(x) =
3
�
−35
f−1(x) =
5
�
−13
f−1(x) =
5
�
+53
View answer 3. What is the domain of the inverse function of f(x) = -x2? x > 0 x < 0 x ≥ 0
x ≤ 0
All real numbers View answer 4. What is the range of the inverse function of f(x) = x3? f−1(x) > 0
f−1(x) < 0
f−1(x) ≥ 0
f−1(x) ≤ 0
All real numbers View answer 5.
In the power function f(x) = -2x3, what is the end behavior of f(x) as x goes to -
∞?
f(x) ➝
-
∞
f(x) ➝
-2 f(x) ➝
0 f(x) ➝
2 f(x) ➝
∞
View answer 6. In the exponential function f(x) = 3−
�
+ 2, what is the end behavior of f(x) as x goes to ∞?
f(x) ➝
-
∞
f(x) ➝
-2 f(x) ➝
0 f(x) ➝
2
f(x) ➝
∞
View answer 7. Evaluate the exponential function f(x) = 52
�
when x = -1. f(-1) = 25
f(-1) = -
25
f(
-
1) =
125
f(-1) = -
125
f(-1) = -10 View answer 8. If algae grows at a rate that can be modeled by the exponential function A(t) = ae
��
, what is the surface area of algae on a pond if the initial area of the algae (a) is 2 square meters, the growth rate (r) is 10%, and the algae grows for three days (t)? (Use a calcualtor or 2.718 for the value of e.) 1.9 2.7
3.2 3.6 4.1 View answer 9. What is the value of log3(27)? 1 3
9 27 Does not exist.
View answer 10. What is the value of log2(-4)? -8 -2 2 8 Does not exist.
View answer 11. What is the value of log4(164)? 14 116 -2 -
3
-4 View answer 12. If f(x) = ln(x), what is the transformation that occurs if g(x) = ln(x + 2)?
Shift 2 to the left.
Shift 2 to the right. Shift 2 up. Shift 2 down. Cannot be determined. View answer 13. If f(x) = log(x), what is the transformation that occurs if g(x) = 3log(x)? Compress by factor of 3. Shift 3 right. Stretch by factor of 3.
Shift 3 down. Cannot be determined. View answer 14. Expand log(3
�
2
�
). 3logx −
2logy log(x3) −
log(y2) 32log(xy) log3 + logx
−
log2
−
logy log(3
�
2
�
) View answer 15.
Simplify 2ln(x + 2) −
ln(x + 2)
−
ln(2) −
3. ln(
�
+22)
−
3
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ln(
�
+25)
ln(
�
+26)
ln(x + 2)
−
ln(6) ln(x + 2)
−
ln(5)
View answer 16. Simplify the expression log5(250).
(Note ���
(10)
���
(5)
≈ 1.4.)
1.4 2.8 3.4
4.6 5.4
View answer 17. What is the end behavior of f(x) in the function f(x) = log(x −
2) as x approaches 2? f(x) ➝
-
∞
f(x) ➝
-2 f(x) ➝
0 f(x) ➝
2 f(x) ➝
∞
View answer 18. What is the value of x in the equation y12 = y2
�
? 2 3 5
6 12 View answer 19. What is the value of x in the equation 316 = 92
�
? 0 2 4
6 8 View answer 20. Solve for x in the equation log
�
(164) = -2. 2 4 8
16 64